The tip of the red giant branch (TRGB) is a promising standard candle for
measuring extragalactic distances, but inaccuracies between ground and Hubble
Space Telescope (HST) system photometry used in its absolute calibration
currently limit its potential. We present the calibration of the TRGB in the
Large Magellanic Cloud (LMC) on the HST/ACS F814W system. We used archival HST
observations of 12 fields in the LMC to derive blending corrections and
photometric transformations for two comparatively low-resolution, ground-based
wide-area imaging surveys of the LMC that are frequently used to measure the
TRGB. We show that measurements of the TRGB in the LMC and in the Small
Magellanic Cloud (SMC) based on these surveys are biased (too bright) by up to
~0.1 mag in the optical due to blending, and that the bias is a function of
local stellar density. The ground-to-HST correction enables us to place the LMC
TRGB zeropoint on the ACS F814W system, which is commonly used for
extragalactic calibrations, while benefiting from the large sample of TRGB
stars from ground-based observations.
We applied the ground-to-HST corrections to the LMC TRGB magnitudes from Jang
& Lee (2017) and obtained an extinction-corrected TRGB magnitude of
I_0=14.507+- 0.012 (stat) +- 0.028 (sys) mag on the ACS F814W system. Using the
geometric distance from Pietrzynski et al. (2019), this corresponds to an
absolute TRGB magnitude of M_F814W=-3.97 +- 0.04 mag. We revisited the method
used by Freedman et al. (2019) to determine the extinction of the TRGB in the
LMC after accounting for the blending measured in the LMC and SMC ground
photometry. We found that blending in their adopted SMC TRGB photometry (from
Zaritsky et al. 2002) caused a ~0.06 mag overestimate of the LMC extinction in
the I band. We determine a value for the Hubble constant of H_0=72.4 +- 1.9
km/s/Mpc for the TRGB+SNe~Ia distance ladder.